I would support adding ENOTCONN under the ConnectionError umbrella. It is caught for shutdown() calls in a few standard library modules. Here is a demo showing how to trigger it (at least on Linux):

from socket import create_connection, SHUT_RDWR
from socketserver import TCPServer, BaseRequestHandler
from threading import Thread

server = TCPServer(("", 0), BaseRequestHandler)
Thread(target=server.serve_forever).start()
client = create_connection(server.server_address)
server.shutdown()  # Ensure server has closed client connection
server.server_close()
client.send(bytes(1))

>>> client.shutdown(SHUT_RDWR)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
OSError: [Errno 107] Transport endpoint is not connected